How to put your Jenkins console output on a GitHub status page?

Question

I am using Jenkins with GitHub. My Jenkins is run on a server and polls the GitHub repo all the time for new commits. When a commit is made, the Jenkins job gets run and I even see the status on GitHub:

However, if I click on Details, it opens the status of the build on Jenkins:

If I want to see why the job failed then I click on "Console Output" on the left

and see the output:

The issue: I would prefer to be able to see the console output on GitHub itself similarly to how you see the status of a GitHub app (for example in the two images below) like this:

edit: or go to this link and check it for yourself.

Is this possible?